Generalized method for rational approximation of SISO/MIMO fractional-order systems using squared magnitude function

Abstract

A new method for the rational approximation of stable/unstable single-input, single-output (SISO)/multiple-input, multiple-output (MIMO) fractional-order systems is proposed. The objective of the proposed algorithm is to obtain an integer-order approximant of an SISO/MIMO fractional-order system. The developed method utilizes the concept of matching of an appropriate number of approximate generalized time moments and approximate generalized Markov parameters of squared magnitude function of fractional-order system to those of approximant. The proposed method preserves the stability/instability property and minimum phase/non-minimum phase characteristics of fractional-order system in the approximant. The method also incorporates a provision for matching the steady-state response of the approximant to that of fractional-order system. Numerical examples consider three cases of approximation, while fractional-order system has the characteristics of (a) stable non-minimum phase SISO, (b) stable non-minimum phase MIMO, and (c) unstable SISO which are presented to validate the efficiency of the proposed method.